As Micca says, this seems to have started with Ewan MacColl, who learned it as an actor and used it -and taught it- as an aid to voice production; it is not a technique that was ever used by traditional singers, being associated only with the revival of the 1950s and later.

As Dave points out, the finger is not usually put in the ear, but the hand cupped slightly behind it; perhaps some people who had only seen the operation from a distance misunderstood what was being done and copied it.  Lightly closing the ear with one finger (no insertion is required) also reduces extraneous sound but is less effective, being mainly useful for making phone calls in noisy places.

Martin Carthy has been known to use the cupped hand method and I've seen others doing it from time to time in folk clubs (and in rock concerts, for that matter), but never, so far as I remember, anybody with a finger in their ear.  Though I don't doubt that there are people out there doing it, sometimes for the wrong reasons, I suspect that the stereotype is usually just a straw man, invented so that it can be more easily knocked down than the real thing.  Constructive criticism is so much harder, after all.